Condensed concepts

Friday, March 16, 2018

Every few years I write a post about problems that email creates. Such a post is here.
Over the past few years, I have become aware that smartphones have reduced the effectiveness and efficiency of email. Many people now read email on a smartphone and this increases the likelihood that
- they read it even faster and so are less likely to digest anything of substance
- they won't open or can't read attachments properly
- they are less likely to reply
- if they do reply, they are more likely to have a knee-jerk response
- it is a less important communication channel that SMS, Messenger, WhatsApp, ...
- they are more likely to forward a message that they should think twice about forwarding
- they will not take the action that the email requests.

If the email message is "Shall we meet at 1pm for lunch?" then none of this matters.
However, there are some email messages that consider weightier matters such a detailed discussion of a scientific question, a proposed new policy of substance, a personal relationship issue, ...

Wednesday, March 14, 2018

They consider the unitary Fermi gas within the framework of Fermi liquid theory. This system undergoes a superfluid transition at a temperature of about 0.17 times T_F (the Fermi temperature). They calculate the shear viscosity as a function of temperature. (I think) the complete temperature dependence is obtained by interpolating between the low-temperature and high-temperature limits.

The motivation for the study is the conjectured universal bound for the ratio of the shear viscosity to the entropy density, based on the AdS-CFT conjecture, beloved by string theorists.

The authors find that the conjectured bound is violated because the viscosity can become arbitrarily small near the superfluid transition due to large scattering from superfluid fluctuations. This is because the mean free path becomes arbitrarily small, i.e. the system is similar to a bad metal.

Monday, March 12, 2018

The paper brings together two fascinating topics I have written about before, spin crossover materials and spin ice. One thing that it is a little worrying and disappointing about spin ice materials is that there seem to be only two (?) of them!
This paper argues that some spin crossover materials may be a new class of materials that realise ice physics (residual entropy, emergent gauge fields, monopoles, ...) Here, the Ising spin variable is the two possible spin states (High Spin and Low Spin). These materials have the potential advantage that they may be tuneable due to the creativity of synthetic chemists.
The mechanism of the interaction between spins is rather unique and interesting. It is not an exchange interaction but rather and effective interaction mediated by the spin-lattice interaction, which in these compounds is arguably large.
It is also interesting that the sign of the frustrating interactions (which are key to the stability of the ice) is determined by the anharmonic potential associated with intermolecular interactions in the spin crossover compound.

From Swansea to Sheffield and Southampton to Strathclyde, universities are now engaged in a spending spree: renovating campuses and building lecture theatres, laboratories, libraries and halls of residence. “What we know is that students and their parents, when they go on open days, they are impressed by shiny buildings,” says Nick Hillman, an adviser to the universities minister David Willetts from 2010 to 2013 who now runs the Higher Education Policy Institute, a think-tank.

But as cranes dominate campus skylines, debts are mounting on vice-chancellors’ ledgers.....

It is happening in Australia too. The picture below is the new building for the Faculty of Business and Law at the University of Newcastle, which was relocated from the suburbs to prime real estate in the city to increase "profile". A faculty member told me that the office space and opportunities to interact with students are much worse than in their old building.

We should not lose sight of a basic truth. The quality of an education is not determined by the "quality" of the buildings on campus but rather by the quality of the people inside the buildings. It is just like how the quality of a scientific paper is not determined by the journal in which it is published in but rather by the contents of the paper. I like the following thought experiment. Suppose you took all of the Harvard faculty and relocated them to the Mediocre Australian University campus, and relocated all the MAU faculty to the Harvard campus. After 3 years where will MAU and Harvard have moved to in the "rankings"?

An important question is what is the relationship (if any) between the two methods?
Given that the two methods are formulated in quite different ways it was not clear to me at all whether these question could be answer in any sort of definitive way.

There is a very nice paper which does answers this question in a precise way, with the bonus of also giving the relationship of both methods with rotationally invariant slave bosons (RISB).

The main results are summarised in the Figure below. A result that is useful and insightful is that DMET corresponds to RISB with the quasi-particle weight set to unity (Z=1). There is then no band narrowing associated with the correlations. Given this is a key aspect of strongly correlated electron systems, I think this is a significant shortcoming of DMET. I am also a bit confused about how DMET can then capture a Mott transition.

Friday, March 2, 2018

Spin crossover (SCO) materials are fascinating and raise many interesting questions.
Here I want to address the underlying physics of why there is a large change in bond length (typically 10-20 per cent) when the spin state of the complex changes. Basically, it is because the ligand field splitting Delta changes significantly with bond length. The change in spin state is associated with electrons moving between from the upper d -levels on the metal ion (e_g in an octahedral complex) to the upper levels (t_g2).

What is the physical origin of this splitting?

How does Delta vary with the distance between the metal (M) and the ligand L?

One can answer the second question theoretically with quantum chemistry computations and experimentally by changing the ligand L, which leads to changes in bond length. The figure below is taken from the book, Ligand Field Theory and its Applications.

Quantum chemistry computations show a similar variation for a given complex by varying the M-L distance. For example, see Figure S5 in the Supplementary Material for this paper.

What is the physical origin of this splitting?

A first guess is from "crystal field theory" that associates the energy level splitting with classic electrostatic effects. This gives a value that falls of as the sixth power of the M-L distance, and makes the concrete (and roughly correct ) prediction that for an octahedral complex the e_g levels move up by 3/2 times the amount that the t_2g levels move down. For a tetrahedral complex the opposite happens. However, there are two significant problems with this prediction. First, the predicted splitting is an order of magnitude too small. Second, this model predicts the opposite trend to the spectrochemical series.

A better description is obtained from "ligand field theory" where the splitting arises from covalent bonding between the d-orbitals on the metal and the p-orbitals on the ligand. For an octahedral complex, the t_2g (e_g) orbitals have positive (zero or negative) overlap with the ligand orbitals.

Aside.

It is interesting (and disturbing?) that the authors of the figure above compare the data for Delta vs. R to power laws, 1/R^6 and 1/R^5. For the data R varies by about 10 per cent. To distinguish between power laws one should be comparing data over several orders of magnitude!

In reality, the data is just as consistent with a linear decay.

What is of interest to me is the magnitude of the decay, G= 1 eV/Angstrom. The next step is to argue why this is "large". The change in bond length with spin crossover will be approximately G/B where B is the elastic constant for the bond.

Wednesday, February 28, 2018

Physicists are notorious for thinking they can revolutionise other fields. The results are often embarrassing. Previously, I considered how to (not) break into a new field. One of the basic points ito remember is that there is a lot of nuance, a lot of rich history, and a lot of very smart hard-working people associated with any worthwhile intellectual endeavour.

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About Me

I have fun at work trying to use quantum many-body theory to understand electronic properties of complex materials.
I am married to the lovely Robin and have two adult children and a dog, Priya (in the photo). I also write an even more personal blog Soli Deo Gloria [thoughts on theology, science, and culture]

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Although I am employed by the University of Queensland and funded by the Australian Research Council all views expressed on this blog are solely my own. They do not reflect the views of any present or past employers, funding agencies, colleagues, organisations, family members, churches, insurance companies, or lawyers I currently have or in the past have had some affiliation with.

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